In the world where people with money overlap with restaurants and try to work out how to make more money, one of the things they talk about is the desire to find "the new pizza". This means a new mass-market product that can be made quickly and eaten both on the premises and as a takeaway. Ideally, this new pizza will be something that can be made fairly cheaply and sold with good margins, and that will appeal to the public as new and modern and as sexy as pizza was when it first burst on the world.

Jamie Oliver's new venture, Union Jacks, is "rolling out", as business types say. The first one was in Holborn; I went to the second one, in Chiswick. There are more to come in Winchester, Covent Garden and, possibly before too long, somewhere near you. Union Jacks focuses on something called "British flatbreads". Are these the new pizza? No, they're not. That's because they're the old pizza. This isn't surprising, because Oliver's partner in this experiment is Chris Bianco, who runs a restaurant in Phoenix, Arizona that has several times been named as making the best pizza in the US. A British flatbread, it turns out, is a pizza made with British ingredients and emphasising "British flavours". That's a slightly cryptic phrase that turns out to mean flavours that we British people like: roast pork with apple sauce and crackling, oxtail, chilli and so on.

After mulling the idea over, I've concluded that I like it. I'm a pizza super-traditionalist who likes margarita, marinara and that's about it – I sometimes stretch to a modern one with parma ham and rocket, but I never respect myself afterwards – but this battle has long, long since been lost. The deconstructed, postmodern pizza has been with us for ages, and the fact is that pretty much every ingredient in the world has been used as a pizza topping, and liked by somebody, somewhere. So what the hell: why should British ingredients be left out?

The issue is whether it works. The new restaurant works already – the downstairs was cramped and chocka with buggies and baby SUVs. Staff are friendly and interested in what they're serving, and the place looks just right, a cross between a British cafe and an Italian pizzeria.

As for whether the pizzas work, it's harder to say. They've really pushed the British flavours: they've gone for it. The "Old Spot" was pork shoulder with quince and bramley sauce, stilton, crackling and watercress. This was a kill-or-die-trying attempt at Britishising the pizza: rich and fatty, though the globs of stilton were a bit weird. I admired its brio without loving the pizza. The "Chilli Freak" had two things I like: an admission that chilli is now a key British flavour and the use of six different types of chilli. That's a great idea, because chillies have such a range of flavour beneath and alongside the heat. But it was simply too hot. Way, way too hot. I'm as chilli-tolerant as anyone I know, but I've never eaten anything as hot as this. I got through half of it, but despite eating all the curd they serve on the side as a cooling condiment, I was in genuine pain. Maybe my first mouthful was all super-hot scotch bonnet, but they're emphasising chilli-heat so much that they're missing out on other flavours. "Red Ox" was oxtail and brisket with red leicester, and that was a better balance, hearty but not cloying; the basic cheese-and-tomato "Juliette" was good, too, and made use of the fact that cheddar and lincolnshire are tangier than mozzarella.

There's plenty else to like. The kids' menu is a drink, a main course and a dessert for a welcome £6. They have retro drinks such as pink cola and dandelion and burdock, and retro puddings such as arctic roll in a sophisticated version with white chocolate (the kids' menu advises, "Ask your parents"). Non pizza-eaters can have a grill: sea bass, simply cooked in a wood oven, with a watercress salad for £11.

The menu makes a point not just of listing suppliers, but also of giving their email contact details, and all the drinks – wines and beers and spirits – are British. I can't think of another chain restaurant that does that. Here's hoping it starts a trend.

•Union Jacks, 217-221 Chiswick High Road, London W4, 020-3617 9988. Open all week, noon-11pm (10.30pm Sun). Meal with drinks and service, about £50 for two.